where \(d_i\)  is the domain label, \(CE\)  denotes the cross-entropy loss function, \(\mathbf {Z}_{i}^\mathcal {D} = \lbrace \mathbf {z}_{i\_1}^\mathcal {D},...,\mathbf {z}_{i\_T}^\mathcal {D}\rbrace \) , \(TrN_i\)  is the \(n\) -frame temporal relation network, \(G_{f}\) , \(G_{r}\) , and \(G_{v}\)  are the frame feature level, the temporal relation feature level, and the video feature level domain classifiers, respectively.
Note that the other ways of integrating frame-level features to video-level features, e.g., using a Graph Convolutional Network (GCN) [1]} as [2]} do, can be straightforwardly applied here.
To this end, we obtain the domain adversarial loss by summing up Eqs. (REF -REF ):
\( \mathcal {L}_{\text{adv}} = \mathcal {L}_{f} + \mathcal {L}_{r} + \mathcal {L}_{v}.\) 
